Wave Speed Formula: Meaning, Properties & Examples

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The wave speed formula involves wavelength and frequency. According to the equation:

v = f λ

where; v is the wave speed in meters per second, m/s. f is the frequency in hertz, Hz. A Wave speed is the distance the wave travels in a given amount of time.

Table of Contents

What is Wave speed?
Properties of a Wave
The formula of Wave Speed
Examples of wave speed
Things to Remember
Previous Year Questions
Sample Questions

Key Terms: Wave, Frequency, Time Period, Wavelength, Wave Speed, Wave Speed Formula, Oscillation, Medium

What is Wave Speed?

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Wave speed is the total distance traveled by a given point on the wave in a given interval of time. An equation to define wave speed is

Speed = Distance / Time

Wave speed according to an equation; if the crest of an ocean wave moves a distance of 50 meters in 10 seconds, then the speed of the ocean wave is 5.0 m/s.

Also Check: Speed, Distance and Time Formula

Properties of a Wave

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Properties of the wave is specified below:

When a source vibrates and disrupts a particle in the medium, this wave is visible. It can also be seen in the case of tuning forks or water ripples when a body is dropped, for example.
The number of waves traveling through a point in a unit of time (second) is called frequency, and the reciprocal of it is the time period of the wave.
The wave's wavelength is the distance it travels in a single time period.
If the crest of an ocean wave moves 20 meters in 10 seconds, the wave's speed is 2.0 meters per second. Also, if the crest of an ocean wave moves 25 meters in 10 seconds, the wave's speed is 2.5 meters per second.

Also Check: Frequency and Wavelength

Wave Speed Formula

Wave Speed Formula

Also Check: Unit Of Wavelenght

The formula of Wave Speed

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The wave speed formula involves wavelength and frequency. This is given by:

v = f λ

Where the symbols are abbreviated as follows:

v represents the velocity of the wave
f is the frequency of the wave
λ is the wavelength

Also Check: Difference between Speed and Velocity

Examples of Wave Speed

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Example 1: The wavelength with which a light wave travels is 600 nm. Determine its frequency.

Solution: Given: Wavelength λ = 600 nm,

Velocity of light v = 3 x 108 m/s²

The frequency is calculated by,

f = v / λ

=3 x 10⁸/600 x 10^-9

f= 5 x 10¹⁴ Hz

The frequency of the light wave is f= 5 x 10¹⁴ Hz

Also Check: Difference between Gravitation and Gravity

Example 2: The wavelength of a sound wave is 1.5 mm. Determine its frequency.

Solution: Given:

Wavelength λ = 1.5 mm,

Velocity of sound v = 343.2 m/s.

The frequency is calculated by,

f = v / λ

= 343.2 /1.5 x 10^-3

f= 228 x 10³ Hz

The frequency of the light wave is f= 228 x 10³ Hz

Things to Remember

A wave is a disturbance or oscillation through a moving medium.
Frequency is the number of waves passing through a point in a unit of time (second), and the reciprocal of that is the wave's time period.
The formula for wave speed is v = f λ.
These relationships and the wave speed formula can be used to determine the unknown values when the remaining values are given.

Also Check: Class 11 Physics Notes

Important PYQ’s Based On Wave Speed Formula

Interference was observed in the interference chamber where... [NEET - 1993]
A wave traveling along a string is described by the equation... [MHT CET - 2008]
For the constructive interference the path difference between... [KCET - 2009]
A person with a vibrating tuning fork of frequency... [KCET - 2013]
An air column, closed at one end and open at the other, resonates... [NEET 2016]

Sample Questions

Ques. Define a Wave. (1 Mark)

Ans: A wave, in physics, can be defined as a disturbance or oscillation that travels across space-time and is associated with an energy transfer. We can observe an ocean wave as it travels across the medium, which is the ocean water. In addition, the crest of the wave may be seen traveling from one site to another over a period.

Ques. What is the relationship between time period and frequency? (1 Mark)

Ans: The number of waves traveling through a point in a unit of time (second) is called frequency, and the reciprocal of it is the time period of the wave. The wave's wavelength is the distance it travels in a single time period.

What is the formula for wave speed? (2 Marks)

Ans: The wave speed formula is given by:

v = f λ

Where, the symbols are abbreviated as follows:

v represents the velocity of the wave
f is the frequency of the wave
λ is the wavelength

Ques. A wave with a frequency of 5 Hz has a speed of 25 m/s. What is the wave’s wavelength? (2 Marks)

Ans: Wave’s wavelength is:

f = 5 Hz

v = 25 m/s

λ = ?

v = λ ⋅f ⇒ λ = v f = 25/5 = 5 m

Ques. A wave having a frequency of 50 Hz, has a wavelength of 10 m. What is the wave's speed? (2 Marks)

Ans: Wave’s speed is

f = 50 Hz

λ =10 m

v =?

v = λ ⋅f = 10⋅50= 500 m/s

Ques. What is the frequency of a wave with a wavelength of 10 m and a speed of 340 m/s? (2 Marks)

Ans:

λ =10 m

v = 340 m/s

f=? v = λ ⋅f ⇒ f = v λ = 340 /10 = 34 Hz

Ques. The speed of a wave is 900 m/s in a certain medium. In 2 minutes, 3000 waves pass over a certain point of the medium. Compute its wavelength. (3 Marks)

Ans: The speed of a wave in medium v = 900 ms^-1

Freq. of wave = no. of waves passing per sec (n) = 3000 waves/2min = 3000 / 2×60 = 25s

Wavelength = λ =?

v = n λ

λ = v/n

A = 900/25 =36m

A = 36m

Answer: λ = 36 m

Ques. The bottom of a ship in the sea shoots SONAR waves straight down into the seawater. After 3.5 seconds, the signal reflects off the deep bottom bedrock and returns to the ship. When the ship has moved 100 km, it transmits another signal, which is received again after 2s. Calculate the depth of the sea in each situation, as well as the height difference between the two. (4 Marks)

Ans: The velocity of SONAR waves in water C = 1500 ms^-1

Time taken by a wave after reflection from the bottom of sea

2t = 3.5s

t =1.75s

Distance covered (d)=?

C = d/t => d = c.t = 1500 × 1.75 - 2625 m

After moving 100km

The time taken by the wave = 2t = 2s

T = 2/2 = 1s

d =?

d = 1500 × l

= 1500

The different between these two heights= 2625 - 1500

= 1125m

Answer: Δd = 1149.75

Ques. Define a wave speed? (1 Mark)

Ans: A wave speed can be described as the total distance traveled by a given point on the wave in a given interval of time. The equation that define wave speed is ‘Speed = Distance / Time’

Ques. Define two features of waves. (2 Marks)

Ans: Features of waves are as follows:

The number of waves traveling through a point in a unit of time (second) is called frequency, and the reciprocal of it is the time period of the wave.
The wave's wavelength is the distance it travels in a single time period.

Chapter Related Articles
Difference between Distance and Displacement	Work, Energy and Power	Motion in a Straight Line
Laws of Motion	Motion	System of Particles & Rotational Motion

Physics Study Guides
NCERT Solutions for Class 11 Physics	NCERT Solutions For Class 6 to 12	Physics MCQs

Wave Speed Formula: Meaning, Properties & Examples

What is Wave Speed?

Properties of a Wave

The formula of Wave Speed

Examples of Wave Speed

Things to Remember

Important PYQ’s Based On Wave Speed Formula

Sample Questions

CBSE CLASS XII Related Questions

1.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

3.
Write any two features of nuclear forces.

5.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

Similar Physics Concepts

Comments

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Wave Speed Formula: Meaning, Properties & Examples

What is Wave Speed?

Properties of a Wave

The formula of Wave Speed

Examples of Wave Speed

Things to Remember

Important PYQ’s Based On Wave Speed Formula

Sample Questions

CBSE CLASS XII Related Questions

1.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

3. Write any two features of nuclear forces.

5.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

2.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

3.
Write any two features of nuclear forces.

5.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be: