An elastic string is stretched between two fixed ends, separated by a distance l.
(a) When the string is made to oscillate at a particular frequency, f0 , a standing wave is formed in the *first harmonic mode*.
- i Outline what is meant by the term *first harmonic mode*.
- ii Sketch a diagram to show the standing wave in the first harmonic mode.
- iii State the wavelength of the standing wave.
(b) The string is now made to oscillate at a larger frequency, and again, a standing wave is formed, this time as the second harmonic.
- i How is the frequency of the second harmonic related to the frequency of the first harmonic mode?
- ii Sketch a diagram to show the standing wave in the second harmonic.
- iii What is the wavelength of the standing wave in the second harmonic?
(c) The string is now made to oscillate at three more, higher frequencies so that standing waves are formed in the third, fourth and fifth harmonics.
- i What will the values of these higher frequencies be compared to that of the first harmonic?
- ii Sketch diagrams to show the standing waves in the third, fourth and fifth harmonics.
- iii If the number of the harmonic is n , and the speed at which waves travel along the stretched string is v , write general equations for the wavelength and the frequency of the standing wave harmonics.