Question

On a standard day the speed of sound is 345 meters per second. A whistle whose frequency is 725 Hz is movingtoward an observer at a speed of 25.2 meters per second. What is the wavelength of the sound at the observer?(a) 0.367 m(b) 0.441 m(c) 0.511 m(d) 0.623 m

Answer 1

Take into account that this is a situation where the source moves presenting the Doppler effect.

In order to determine the wavelength of the sound generatd by the whistle at the observer, first calculate the frequency at the observer by using the following formula:

`f=(v)/(v-v_s)f_s`

where:

f: frequency at the observer = ?

fo: source frequency = 725 Hz

vs: source speed = 25.2 m/s

v: speed of sound = 345 m/s

replace the previous values of the parameters into the fomrula for f:

`\begin{gathered} f=(345m/s)/(345m/s-25.2m/s)725Hz \\ f=782.1Hz \end{gathered}`

Next, use the following formula to determine the wavelength of the sound at observer, by using the previous result:

`\lambda=(v)/(f_s)=(345m/s)/(782.1Hz)=0.441m`

Hence, the wavelength of the sound at the observer is 0.441 m