A string under tension τi oscillates in the third harmonic at frequency f3, and the waves on the

step 1 16 .42. So we have a string under some initial tension oscillating in its third harmonic, which

A string under tension τi oscillates in the third harmonic...

A string under tension $\tau_{i}$ oscillates in the third harmonic at frequency $f_{3},$ and the waves on the string have wavelength $\lambda_{3}$ . If the tension is increased to $\tau_{f}=4 \tau_{i}$ and the string is again made to oscillate in the third harmonic, what then are (a) the frequency of oscillation in terms of $f_{3}$ and (b) the wavelength of the waves in terms of $\lambda_{3} ?$

A string under tension $\tau_{i}$ oscillates in the third harmonic at frequency $f_{3},$ and the waves on the string have wavelength $\lambda_{3}$ . If the tension is increased to $\tau_{f}=4 \tau_{i}$ and the string is again made to oscillate in
the third harmonic, what then are (a) the frequency of oscillation in
terms of $f_{3}$ and (b) the wavelength of the waves in terms of $\lambda_{3} ?$

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Key Concepts

Relationship between Frequency, Wavelength, and Wave Speed

The fundamental wave equation relates frequency, wavelength, and wave speed via the relation f = v/?. When the tension is increased in the string, the wave speed increases, leading to an increase in frequency if the wavelength is fixed by the standing wave conditions.

Standing Waves on a String

Standing waves are formed on a string fixed at both ends, where only specific wavelengths and frequencies (harmonics) are allowed. The wavelength for a particular harmonic is determined solely by the length of the string and the harmonic number, and does not change when other parameters, like tension, are varied.

Wave Speed on a String

The speed of a wave traveling along a string is given by v = ?(tension/linear density). Thus, when the tension is increased, the wave speed increases proportionally to the square root of the tension change, affecting the frequency of the standing waves.

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