A tuning fork with natural frequency begins vibrating at

Chapter , Problem 67

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A tuning fork with natural frequency begins vibrating at time and is stopped after a time interval, The waveform of the sound at some later time is shown (Figure 16-35) as a function of Let be an estimate of the number of cycles in this waveform. (a) If is the length in space of this wave packet, what is the range in wave numbers of the packet? (b) Estimate the average value of the wavelength in terms of and (c) Estimate the average wave number in terms of and (d) If is the time it takes the wave packet to pass a point in space, what is the range in angular frequencies of the packet? (e) Express in terms of and ( f) The number is uncertain by about cycle. Use Figure 16-35 to explain why. ( g) Show that the uncertainty in the wave number due to the uncertainty in N is 2p>x. SSM