Question

On the planet Arrakis, an ornk is flying toward a fellow stationary ornk at 25 m/s while singing at a frequency of 1200 Hz. If the second ornk hears a tone of 1240 Hz, what is the speed of sound in the atmosphere of Arrakis?

Answer 1

The speed of sound in the atmosphere of Arrakis is 775 m/s.

Step-by-step explanation:

Given that,

Frequency f= 1200 Hz

Second frequency f' = 1240 Hz

Speed = 25 m/s

We need to calculate the speed of sound in the atmosphere of Arrakis

Using formula of frequency

`f'=(v)/(v-v_(s))f`

`f'(v-v_(s))=vf`

`v=(f'v_(s))/(f'-f)`

Where,
`v_(s)` = speed of the sound

v = speed of the listener

Put the value into the formula

`v=((1240*25)/(1240-1200))`

`v=775\ m/s`

Hence, The speed of sound in the atmosphere of Arrakis is 775 m/s.

Answer 2

775 m/s

Step-by-step explanation:

v = Velocity of sound

f' = Observed frequency = 1240 Hz

f = Actual frequency = 1200 Hz

`v_s` = Relative speed of the train = 25 m/s

From the Doppler effect we get the relation

`f'=f(v)/(v-v_s)\\\Rightarrow v=(f'v_s)/(f'-f)\\\Rightarrow v=(1240* 25)/(1240-1200)\\\Rightarrow v=775\ m/s`

The speed of sound in the atmosphere of Arrakis is 775 m/s