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Sound waves travel at 350 m/s through warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air
A
Decreases by a factor 20
B
Decreases by a factor 10
C
Increases by a factor 20
D
Increases by a factor 10
Detailed Solution
When a wave passes from one medium to another, its frequency does not change; it stays 700 Hz.
Since $v = \nu\lambda$ and $\nu$ is constant, $\lambda \propto v$.
In air: $\lambda_{air} = \frac{350}{700} = 0.5$ m
In brass: $\lambda_{brass} = \frac{3500}{700} = 5$ m
$\frac{\lambda_{brass}}{\lambda_{air}} = \frac{5}{0.5} = 10$
So the wavelength increases by a factor 10.
Since $v = \nu\lambda$ and $\nu$ is constant, $\lambda \propto v$.
In air: $\lambda_{air} = \frac{350}{700} = 0.5$ m
In brass: $\lambda_{brass} = \frac{3500}{700} = 5$ m
$\frac{\lambda_{brass}}{\lambda_{air}} = \frac{5}{0.5} = 10$
So the wavelength increases by a factor 10.