Q53E - University Physics with Modern Physics

Question

Two swift canaries fly toward each other, each moving at 15.0 m/s relative to the ground, each warbling a note of frequency 1750 Hz. (a) What frequency note does each bird hear from the other one? (b) What wavelength will each canary measure for the note from the other one?

Step-by-Step Solution

Answer

a) Frequency is $f_b=1910\mathrm{Hz}$ 

b) Wavelength measured ${\lambda }_{in front}=0.188m$

Step 1:

a) The frequency detected by each bird is;

$f_b=f_s\left(\frac{v\pm v_b}{v+v_s}\right)$

Given data:

Speed of sound in air $v=344m/s$

Speed of bird that is considered as an observer $v_b=15m/s$

Speed of bird that is considered the source $V_s=15m/s$

Frequency of sound emitted by birds as a source $f_s=1750\mathrm{Hz}$

Frequency of sound detected by other bird  $f_b$

On putting the values;

$\begin{array}{l}{f}_b=\left(1750Hz\right)\times \frac{(344m/s)+(15\mathrm{m}/\mathrm{s})}{(344\mathrm{m}/s)-(15m/s)}\\ f_b=1910Hz\end{array}$

Hence, the frequency is $f_b=1910Hz$

Step 2:

b) The wavelength in front either of any of the two birds is expressed as;

${\lambda }_{infront}=\frac{v-v_S}{f_s}$

On putting the values;

$$\begin{gathered} {\mathrm{\lambda }}_{\mathrm{infront}}=\frac{\left(344\mathrm{m}/\mathrm{s}\right)+\left(15\mathrm{m}/\mathrm{s}\right)}{1750\mathrm{Hz}} \\ {\mathrm{\lambda }}_{\mathrm{infront}}=0.188\mathrm{m} \end{gathered}$$

Hence, the wavelength measured ${\mathrm{\lambda }}_{\mathrm{infront}}=0.188\mathrm{m}$