Propagation Of Sound Wave

Numericals

Q 1) The heart of a man beats 75 times a minute. What is its (a) frequency and (b) time period?

Ans : (a) Number of times, the heart beats in 1minute or 60 seconds = 75

Number of times, the heart beats in one second i.e. frequency of the heart,

n = 75/60 s-1 = 1.25 s-1

(b) Time period of the heart , T = 1/n = 1/1.25 = 0.8s

Q 2) The time period of a simple pendulum is 2 s. Find its frequency.

Ans.

n = 1/T

= 1/2s-1 = 0.5 s-1

= 0.5 Hz

Q 3) The Separation between two consecutive crests in a transverse wave is 100 m. If wave velocity is 20 ms-1. Find the frequency of wave.

Ans : Here λ = 100 m , v = 20 m/s n = ?

Using v = nλ

n = v/λ

= 20 / 100 Hz = 0.2 Hz

Q 4) A longitudinal wave travels at a speed of 0.3 m/sand the frequency of wave is 20 Hz. Find the separation between the two consecutive compressions.

Ans : Here v = 0.3 m/s ; n = 20 Hz

Let separation between two consecutive compressions i.e. wave-length of the wave = 1

Using v = nλ

λ = v/n = 0.3/20 m = 1.5 * 10-2

= 1.5 cm

Q 5) A source of wave produces 40 crests and to troughs in 0.4s. What is the frequency of wave?

Ans : Number of crests and troughs produced in 0.4s = 40

Number of crests and troughs produced in 1s = 40 /0.4 = 100

i.e. Frequency of the wave = 100 Hz

Q 6) An observer A fires a gun and another observer B at a distance 1650 m away from A hears its sound. If the speed of sound is 330 m/s. Find the time when B will hear the sound after firing by A.

Ans : Distance to be travelled by sound = 1650 m

Velocity of sound = 3330 m/s

Time = distance / velocity = 1650 / 330 = 5 s

Time after which B will hear the sound after firing by A = 5s

Q 7) The time interval between a lightning flash and the first sound of thunder is 5 s. If the speed of sound in air is 330 m/s, find the distance of flash from the observer.

Ans : Here, t = 5s

Speed of sound V = 330 m/s

Distance of the flash from the observer d = V * t

distance = 330 * 5 = 1650 m

Q 8) A boy fires a gun and another boy at a distance hears the sound of fire 2.5 s after seeing the flash. If speed of sound in air is 340 m/s. Find distance between the boys.

Ans : We know that, Speed = distance travelled / time taken

distance = speed * time = 2.5 * 340 = 850 m

Q 9) An observer siting in line of two tanks, watches the flashes of two tanks firing at each other at the same time, but he hears the sounds of two shots 2s and 3.5 s after seeing the flashes. If distance between the two tanks is 510m, find the speed of sound.

Ans : Let distance of first tank from the observer = x1 metre

distance of the second tank from the observer = x2 metre

x2 - x1 = 510 m

Let speed of sound = v m/s = ?

distance = speed / time

x1 = v * 2 = 2v and x2 = v * 3.5 = 3,5 v

x2 - x1 = 3.5v - 2v

510 = 1.5 v

v = 510 / 1.5 m/s = 340 m/s

Q 10 ) How long will sound take to travel in ( a) an iron rail and ( b) air, both 3.3 km in length? Take speed of sound in air to be 330 m/s and in iron to be 5280 m/s.

Ans : Distance to be travelled by sound = 3.3 km = 3300 m

Time taken by sound to travel in iron rail = Distance / Velocity of sound in iron

= 3300 / 5280

= 0.625 s

Time taken by sound to travel in air = Distance / Velocity of sound in air

= 3300 / 330

= 10 s

Q 11) Assuming the speed of sound in air equal to 340 m/s and in water equal to 1360 m/s, find the time taken to travel a distance 1700 m by sound in (i) air and (ii) water.

Ans : (i) Time taken by sound to travel a distance of 1700 m in air

= Distance / Velocity of sound in air

= 1700 / 340 = 5s

(ii) Time taken by sound to travel a distance of 1700 m in water

= Distance / Velocity of sound in water

= 1700 / 1360 = 1.25 s

Q 12) Ocean waves of time period 10 s have velocity 15 m/s. Find (i) the wavelength of these waves.

(ii) the horizontal distance between a wave crest and its adjoining wave trough.

Ans : (i) T = 10 s , V = 15 m/s

V = λ / T

λ = V * T

= 15 * 10 = 150 m

(ii) The distance between a wave crest and its adjoining wave trough

= λ / 2 = 1/2 *150 = 75m

Q 13) A wave pulse of frequency 200 Hz , on a string moves a distance 8 m in 0.05 s.

Calculate : (a) The velocity of pulse

(b) the wavelength of wave on string

Ans : Given d = 8 m, t = 0.05 s, f = 200 Hz

(a) The velocity of pulse V = Distance moved d/ Time taken t

V = 8 m / 0.05s = 160 m/s

(b) Wave velocity on string V = velocity of wave pulse on it = 160 m/s

from relation, V = f λ ,

λ = V/f = 160 / 200 = 0.8 m

Q 14) Compare approximately the speed of sound in air and steel.

Ans : The speed of sound in air is nearly 330 m/s and in steel is nearly 5100 m/s. Thus the ratio of speed of sound in air and steel = Speed of sound in air / Speed of sound in steel

Speed of sound in air / Speed of sound in steel

= 330/5100

= 1/15 nearly

Q 15) The smoke from the gun barrel is seen 2 second before the explosion is heard. If the speed of sound in air is 340 m/s , calculate the distance of observer from gun. State the approximation used.

Ans : Given : Speed of sound = 340 m/s , time = 2s

Speed = distance travelled / time taken

Distance = speed * time

= 340 * 2 = 680 m

Propagation Of Sound Wave - Physics Numericals Class 9