First slide

Stationary waves

Question

In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m³. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become (take g = 10 ms^–2)

Moderate

A

240 Hz
B

230 Hz
C

220 Hz
D

200 Hz

Solution

$n = \frac{p}{2 l} \sqrt{\frac{T}{m}} \propto \sqrt{T} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\Rightarrow \frac{260}{n_{2}} = \sqrt{\frac{50 .7 g}{(50 .7 - 0 .0075 \times 10^{3}) g}} \Rightarrow n_{2} \approx 240 Hz$

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