Chapter 2: Q53E (page 541)

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?

Expert verified

a) Frequency is $f_{b} = 1910 Hz$

b) Wavelength measured $λ_{i n f r o n t} = 0.188 m$

Step by step solution

a) The frequency detected by each bird is;

$f_{b} = f_{s} (\frac{v \pm v_{b}}{v + v_{s}})$

Given data:

Speed of sound in air $v = 344 m / s$

Speed of bird that is considered as an observer $v_{b} = 15 m / s$

Speed of bird that is considered the source $V_{s} = 15 m / s$

Frequency of sound emitted by birds as a source $f_{s} = 1750 Hz$

Frequency of sound detected by other bird $f_{b}$

On putting the values;

$\begin{array}{l} f_{b} = (1750 H z) \times \frac{(344 m / s) + (15 m / s)}{(344 m / s) - (15 m / s)} \\ f_{b} = 1910 H z \end{array}$

Hence, the frequency is $f_{b} = 1910 H z$

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

$λ_{i n f r o n t} = \frac{v - v_{S}}{f_{s}}$

On putting the values;

$λ_{infront} = \frac{(344 m / s) + (15 m / s)}{1750 Hz} λ_{infront} = 0.188 m$

Hence, the wavelength measured $λ_{infront} = 0.188 m$

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