First slide

Charaterstics of sound

Question

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to $4.00 \times 10^{- 2} kg / m$ . If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate is (take $π^{2} = 10$ ):

Difficult

A

45.3
B

50 Hz
C

30 Hz
D

62.3 Hz

Solution

P = $\frac{1}{2} {μω}^{2} A^{2} v$
using v = $\sqrt{\frac{T}{μ}}$
$\Rightarrow ω = \sqrt{\frac{2 P}{A^{2} \sqrt{Tμ}}}$
$f = \frac{ω}{2 π} = \frac{1}{2 π} \sqrt{\frac{2 P}{A^{2} \sqrt{Tμ}}}$
using data f = 30 Hz.

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