Observe and explain Observe the series of sketches at the ri

Observe and explain Observe the series of sketches at the right. The pulses travel at speed v along the string of length L. Based on your analysis and using these two quantities, decide the time interval T_1 (called the period for the first vibration) between upward pulls of the hand so that each upward pull supports or enhances the pulse that has just returned to and reflected from your hand after one trip down the string and back. The frequency of these upward pulls is f_1 = 1/T_1. The vibration that is produced is called the fundamental or first harmonic standing wave vibration, and its frequency is labeled f_1.

Solution

From the figures given Position L makes the string to vibrate in its natural frequency

The string vibration makes a half-wave

wavelength = 2L

frequency of the wave f = v/2L

for the hand pulls to support the wave motion, the frequency must be in resonance with the string frequency i.e. v/2L

The period T = 1/f = 2L/v