Sine waves are sent down a $1\mathrm{.}9$ m long string fixed at both ends. The waves reflect back in the opposite direction. The amplitude of the wave is $4\mathrm{.}40$ cm$.$ The propagation velocity of the waves is $160$ m$/$s$.$ The

n $=6$

resonance mode of the string is produced. Write an equation for the resulting standing wave.

Answer rating: 100% (QA)

Standing Wave Equation for the String Since the string is fixed at both endsonly specific wavelengths will produce standing wavesThese wavelengths correspond to resonance modes Given Information Length of the string L 19 m Amplitude A 440 cm 0044 m Propagation velocity v 160 ms Resonance mode n 6 Deriving the Equation Resonance Condition in FixedEnd Strings In a fixedend stringthe allowed wavelengths for standing waves satisfy the following condition 2L n where n is an integer representing the resonance mode 1 for the fundamental mode2 for the first overtoneetc Solving for Wavelength Substitute the given values 2 19 m 6 0633 m Standing Wave Equation The general equation for a standing wave on a string can be expressed as yxt A sinkx cost where yxt is the displacement of a point on the string at position x and time t A is the amplitude of the wave k is the wave number k 2 is the phase constant depends on initial conditions omega is the angular frequency 2fwhere f is the frequency Wave Number k k 2 2 0633 m 994 radm Frequency f We can use the relationship between wave velocity vwavelength ... View the full answer