A girl stands 170 m away from a high wall and claps her hands at a steady rate so that each clap coincides with the echo of the one before. a) If she makes 60 claps in 1 min, what value should be the speed of sound in air? b) Now, she moves to another location and finds that she should now make 45 claps in 1 min to coincide with succesaive echoes. calculate her distance from the new position from the wall?
Answers
Answer:
a. Speed = 340 m/s
b. Distance = 255 m
Explanation:
a. Finding the speed of the sound in air
Distance between the girl and the wall is 170 m
She makes 60 claps per min i.e., 60 claps in 60 seconds [since 1 min = 60 sec]
So, frequency of the sound of the clap = 60 / 60 = 1 Hz = 1 per second …. [∵ 1 Hz = 1/second]
Since the sound of the clap will first go to the wall and then reflect back to the girl, therefore the wavelength of the clap = 2 * 170 m = 340 m
∴ Speed of the sound of the clap in the air,
= frequency * wavelength
= (1/sec) * 340 m
= 340 m/s
b. Finding the distance of her for the new position from the wall
Here, she makes 45 claps in per min, 45 claps in 60 secs.
So, the frequency of the sound of the clap
= 45/60
= 0.75 Hz
= 1/0.75
= 1.333 per second
∴ The wavelength or the distance of her for the new position from the wall,
= (speed of the sound of the clap) / (frequency)
= (340 m/s) / (1.333 per sec)
= 255 m