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I have many confusions regarding standing waves. Firstly, will the frequency of standing waves be the same as the emitted waves that make up the standing wave?

What about wavelength? Will wavelength of standing waves be different from the emitted waves making up the standing waves?

Also, if temperature changes, we know that wavelength of the waves will change and frequency will remain constant? Is the same true for stationary waves as well?

Please explain in simple terms, I am only in grade 11!

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  • $\begingroup$ How are your standing waves being produced? Do you have a particular set-up in mind? $\endgroup$ Mar 27, 2023 at 7:29
  • $\begingroup$ It seems likely from your most recent question on standing waves that you were thinking of using a vibration generator or a tuning fork, which sends out 'pure tones', that is sinusoids of a single frequency. My answer below assumes standing waves of the string's or pipe's natural frequency. Such standing waves can ve produced, for example, by twanging a string or blowing over the open end of a pipe. Such disturbances can be resolved into a sum of sinusoids of different frequencies, one of which will be the string's or pipe's natural frequency, and will result in standing waves of this freq.. $\endgroup$ Apr 2, 2023 at 16:04

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(a) "will the frequency of standing waves be the same as the emitted waves [perhaps you mean progressive waves] that make up the standing wave?" Yes. The frequency is that of the oscillations at any point in the wave.

(b) "Will wavelength of standing waves be different from [that of] the emitted waves making up the standing waves?" No, because what we MEAN by the wavelength of a standing wave is the wavelength of the progressive waves of equal wavelength travelling in opposite directions whose superposition forms the standing wave.

(c) "if temperature changes, we know that wavelength of the waves will change [...]" This is usually not the case, or is a very small effect indeed. The wavelength of the standing wave is determined by the geometry of the pipe or whatever it is that constrains the standing wave by causing wave reflections. (e.g. for a pipe of length $L$ closed at one end, $\lambda =\frac {4L}{2n+1}$.) Suggest you re-read my answer to your previous question about standing waves.

(d) "if temperature changes, [...] frequency will remain constant?" Are you thinking about standing sound waves in pipes? If so, raising the temperature will raise the speed ($v$) of sound in air and will therefore raise the frequencies of the standing waves, which are given (for a pipe of length $L$ closed at one end) by $$f=\frac v \lambda=\frac{v(2n+1)}{4L}$$

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  • $\begingroup$ (b) assumes that the propagation medium is homogeneous; if the radiator is embedded in a medium with varying phase velocity then the wavelength of the propagating waves and thus that of the standing waves, as well, will depend on location. $\endgroup$
    – hyportnex
    Mar 25, 2023 at 13:51
  • $\begingroup$ I'm assuming a homogeneous medium as I judged that Nawaz_04 needed a fairly elementary treatment of standing waves. $\endgroup$ Mar 27, 2023 at 14:33

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