Wave Motion Problems and Objective Type Questions

Solved Problems:

1. If the frequency of tuning fork is 400Hz and the velocity 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 = ?
                             No. of vibration made = 30
By using the relation ,                           v = nλ
                                                           λ = v/n = 320/400 = 0.8 m
Distance travelled by sound =  Wavelength X No. of  Vibrations
                                         = 0.8 X 30
                                         = 24.0 m (Ans.)

2. A tuning fork produces sound waves of wavelength 68 cm. If the velocity of sound is 340 m/s. What is the frequency of tuning fork ?
Solution: Here,            wavelength, λ = 68 cm =0.68 m

                          velocity of sound, v = 320 m s⁻¹

Applying the relation,                     v = nλ
                                                340 = n X 0.68
                                                   n = 340 / 0.68  = 500 Hz. (Ans.)

3. A body vibrating with certain frequency sends waves 1.5 m long through a 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:     Suppose frequency of the vibrating body = n

In medium A. wavelength, λ1= 1.5 m

                         velocity, v1 = 120 m s⁻¹

                                                        ^{n = v1 /} λ1 

                                              = 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.(Ans.)}

^{4. A tuning fork makes one complete vibration in 1/200 second and the velocity of sound waves is 340 m/s. Find 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 = ?

Applying the relation,     v = nλ

                                    λ = v / n = 340/200 = 1.7 m (Ans.)

5. 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 , find 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 = v/n  =330/512 =0.644m (Ans.)

6. The velocity of radio waves is 3 × 108 m s−1. Find the wavelength of radio waves being broadcast at a frequency of 500 KHz.
Solution:   Here, 
                        Velocity of radio waves, v = 3 × 108 m s−1
                         Frequency, n = 500 KHz = 500,000 Hz 
                         Wave length, λ = ?
 Applying the relation,             v = nλ
 we get,     WaveLength, λ = v/n 
                                       = 3 × 108 /500000 = 600m (Ans.)

Multiple Choice Questions:

1. In a mechanical transverse wave, the particles of the medium
a. Vibrate 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.With sound waves one cannot observe the phenomenon of 
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 

4. 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.

6. Of the following the wave transmit from one place to another.
a. Mass                    b. Amplitude
c. Momentum           d. Energy

7. A transverse wave has wavelength of 8.0 meters and frequency 200 Hertz. The wave velocity will bear-
a. 1600 m/s              b. 3200 m/s
c. 400 m/s                d. 25 m/s

8. Waves which can propagate through vacuum are
a. Elastic waves        b. Sound waves
c. E.M waves            d. None of these

9. Longitudinal waves are produced in 
a. solids only           b. liquids only
c. gas only              d. in all three states

10. Longitudinal waves cannot travel through
a. vacuum              b. solids
c. liquids                d. gases

11. Hertz is the unit of :
a. frequency                      b. energy 
c. magnetic permeability    d. electric field strength

12. Which of the following  is a longitudinal wave ?
a. Waves on plucked string          b.Water waves
c. Sound Waves                          d. Light waves

13. A thunder clap follows the light flash because light 
a. travels faster than sound     b. is produced first 
c. is easily visible from far       d. travels slower than sound.

14. What will be frequency of a tuning fork producing sound waves of 68 cm? { v= 340 m/s}
a. 5 Hz                 b. 500 Hz
c. 4 Hz                 d. 340 Hz

15. A radio station broadcasts at a frequency of 12 MHz, the wavelength of radio waves will be
a. 2.5 m                b. 25 m
c. 250 m               d. 0.25 m

16. If the velocity of light in Vacuum is 3 × 108 m s−1.Then the velocity of sound waves in vacuum will be

a. 330 m/s            b. 1428 m/s

c. 1728 m/s          d. None of these

17.A tuning fork vibrates with a frequency of 356 Hz to produce sound waves which travel through air with a velocity of 330 m/s. The wavelength of sound  waves produced will be

a. 0.644 m            b. 330 m

c. 0.93 m              d. 0.093 m

18. A wave train moving along a rope has a velocity of 100 m/s and wavelength of 20 m. What is its time period ?

a. 5 sec                   b. 1/5 sec

c. 20 sec                 d. 100 sec

Answers:
1. a
2. d
3. c
4. b
5. a
6. d
7. a
8. c
9. d
10. a
11. a
12. c
13. a
14. b
15. b
16. d
17. c
18. b