A Pipe open at one end has length $0.8$ m. At the open end of the tube a string $0.5$ m long is vibrating in its first overtone and resonates with fundamental frequency of pipe. If tension in the string is $50$ N, the mass of string is (Neglect end correction) (Speed of sound $= 320$ m/s)

Question

A steel wire with mass per unit length $ 7.0 \times 10^{-3} \, \text{kg/m} $ is under a tension of $ 70 \, \text{N} $. The speed of transverse waves in the wire will be:

Answer 1

Step 1: Wave speed on string:
For the second harmonic, the wavelength is the string length, $\lambda=0.5$ m. So $v_s=f\lambda=100\times0.5=50$ m/s.

Step 2: Use v = sqrt(T/mu):
$50=\sqrt{50/\mu}$, so $\mu=\dfrac{50}{2500}=0.02$ kg/m.

Step 3: Mass:
$0.02\times0.5=0.01$ kg $=10$ g. Option (C).

Final Answer:
The string wave speed is 50 m/s, so mu = 0.02 kg/m. \[ \boxed{C} \]

A Pipe open at one end has length \(0.8\) m. At the open end of the tube a string \(0.5\) m long is vibrating in its first overtone and resonates with fundamental frequency of pipe. If tension in the string is \(50\) N, the mass of string is (Neglect end correction) (Speed of sound \(= 320\) m/s)

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The Correct Option is C

Solution and Explanation

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