A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the wave speed?

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BlackTom AI · Accepted Answer

To start, note the given data: frequency f = 690 Hz and the length of the string L = 60 cm = 0.60 m. In a standing wave on a string with both ends fixed, the length of the string accommodates an integer number of half-wavelengths. The diagram shows three loops (three antinodes) along the length, which corresponds to n = 3 half-wavelengths fitting into L. The relationship between length, wavelength, and the number of half-wavelengths is L = n(λ/2), which rearranges to λ = 2L/n.

Substitute the known values: λ = 2 × 0.60 m / 3 = 1.20 m / 3 = 0.40 m.

Next, use the wave speed formula v = fλ. With f = 690 Hz and λ = 0.40 m, we get v = 690 × 0.40 = 276 m/s.

Evaluating the options, the result 276 m/s matches the third choice when listed as a numerical value.

If you’re not seeing the same setup, reconsider how standing waves on a string relate the length to half-wavelengths: each loop corresponds to a half-wavelength, so counting loops helps determine n, which then locks in λ via λ = 2L/n and finally v via v = fλ.

Another way to think about it: increasing the number of loops (for a fixed length) decreases λ, and since frequency is fixed at 690 Hz, v must adjust accordingly through v = fλ. The pattern in the figure clearly indicates three half-wavelengths fit into the 0.60 m length, leading to the 0.40 m wavelength and the resulting speed.

SPHY001 Practice Quiz - Unit 17 | LA057

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the wave speed?

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