An elastic string is stretched between two fixed ends, separated by a distance l.
a. 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. 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. 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.