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# Wave Motion Problems and Objective Type Questions

## 1. the frequency of tuning fork is 400 Hz and the speed of sound in air is 320 m/s, find how far the sound travels while the tuning fork makes 30 vibrations.

Solution:    Given,               Frequency, n =  400Hz                                velocity of sound, v = 320 m/s                                        wavelength, λ = ?
By using the formula,                           v = nλ
λ = v/n =\frac{320}{400}=0.8m
Distance travelled by sound =  Wavelength X No. of  Vibrations
= 0.8 X 30
= 24 m

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## 2. A body vibrating with a certain frequency sends waves 1.5 m long through medium A and 2.0 m long through medium B. The velocity of waves in A is 120 m/s. Find the velocity in B.

Solution: let frequency of the vibrating body = n
In the medium A. wavelength, λ1= 1.5 m
velocity, v1 = 120 m s−1
n = v1 / λ1

\frac{120}{1.5}

= 80 Hz
In medium B. Frequency, n = 80Hz
wavelength, λ2 = 2.0 m
therefore, velocity, v2 = n X λ2
= 80 X 2.0
= 160.0 m s−1
hence velocity of the waves in medium B = 160 m/s

## 3. A tuning fork produces sound waves of wavelength 68 cm. If the speed of sound is 340 m/s. What is the frequency of the tuning fork?

Solution: Here,            wavelength, λ = 68 cm =0.68 m
velocity of sound, v = 320 m s−1

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Applying the relation,                     v = nλ
340 = n X 0.68
n = \frac{340}{0.68}=500 Hz.

## 4. If a tuning fork vibrates with a frequency of 512 Hz to produce sound waves which travel with a velocity of 330 m s−1 , calculate the wavelength ?

Solution: Here, frequency, n = 512 Hz
velocity of sound, v = 330 m s−1
Wave length, λ = ?
using the relation , v = nλ

λ = \frac{v}{n}=\frac{330}{512}=0.644m

## 5. A tuning fork makes one complete vibration in 1/200 second and the velocity of sound waves is 340 m/s. Calculate the wavelength of the sound given out by the tuning fork.

Solution:   velocity of sound, v = 340 m/s                         Time Period, T = 1/200 second
therefore,    Frequency, n = 1/T = 200 vib./second                Wave length, λ = ?

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Applying the relation,     v = nλ                                    λ = v / n =340/200= 1.7 m

## 6.Find the frequency, period and wave number for a light of wavelength 6000 A.U.

Solution velocity of light c=v\lambda Where v is the frequency of light wave and \lambda the wavelength

v=\frac{c}{\lambda}=\frac{3\times10^8}{6000\times10^{-10}}=5\times10^{14}Hz
Period ,\; T= \frac{1} {v}=\frac{1}{5 \times 10^{14}} =2 \times10^{-15} \, second
Wave\, Number,\; = \frac{1} {\lambda}= \frac{1} {6000 \times 10^{-10}}=1.7 \times 10^{6} \,m^{-1}

## 1. In a mechanical transverse wave, the particles of the medium

aVibrate in a direction perpendicular to the direction of propagation of wave.
b. Vibrate in a direction parallel to the direction of propagation of wave.
c. Move in a circle.
d. Move in ellipse.

## 2.One cannot observe the phenomenon of sound waves

a.Refraction              b.Interference
c.Diffraction              d. Polarisation

## 3.Water waves are

a. Longitudinal                                   b. Transverse
c. Both longitudinal and transverse      d. None of these

## Transverse waves cannot be produced in gases because gases-

a. are light                        b. have no elasticity of shape
c. can flow quickly             d. are compressible

## 5. In a mechanical longitudinal wave, the particles of the medium

a. Vibrate in a direction parallel to the direction of propagation of wave.
b. Vibrate in a direction perpendicular to the direction of propagation of wave.
c. Vibrate in circles.
d. None of these.

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