Question

An object of mass is used to provide tension in a 6.0 ‑m‑long string that has a mass of 0.252 kg, as shown. A standing wave that has a wavelength equal to 1.5 m is produced by a source that vibrates at 24 Hz.

Answer 1

The tension on the string at the given length and mass is 54.43 N.

The given parameters:

• length of the string, L = 6.0 m
• mass of the string, m = 0.252 kg
• wavelength, λ = 1.5 m
• frequency of the source, F = 24 Hz

The speed of the wave is calculated as follows;

$v= f\lambda\\\\v = 24 \times 1.5\\\\v = 36 \ m/s$

The tension on the string is calculated as follows;

$v = \sqrt{\frac{T}{\mu} } \\\\v = \sqrt{\frac{T}{M/l} } \\\\v = \sqrt{\frac{Tl}{M} } \\\\v^2 = \frac{Tl}{M} \\\\T = \frac{v^2 M}{l} \\\\T = \frac{(36)^2 \times 0.252}{6} \\\\T = 54.43 \ N$

Thus, the tension on the string at the given length and mass is 54.43 N.

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An object of mass is used to provide tension in a 6.0 ‑m‑long string that has a mass of 0.252 kg, as shown. A standing wave that has a wavelength equal to 1.5 m is produced by a source that vibrates at 24 Hz. Determine the tension on the string.

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