Question

To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M as shown in the figure above. The value of M is such that the standing wave pattern has four "loops." The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1.20 m. The linear density of the string is 1.0 x 10^–4 kg/m, and remains constant throughout the experiment. 

a. Determine the wavelength of the standing wave. 

b. Determine the speed of transverse waves along the string. 

c. The speed of waves along the string increases with increasing tension in the string. Indicate whether the value of M should be increased or decreased in order to double the number of loops in the standing wave pattern. Justify your answer. 

d. If a point on the string at an antinode moves a total vertical distance of 4 cm during one complete cycle, what is the amplitude of the standing wave?

Answer 1

(a) λ = dist / cycles = 1.2 m / 4 = 0.60 m

(b) v = f λ = (120)(0.60) = 72 m/s

(c) More ‘loops’ means a smaller wavelength. The frequency of the tuning fork is constant. Based on v = f λ, less speed would be required to make smaller wavelength. Since speed is based on tension, less M, makes less speed.

(d) In one full cycle, a point on a wave covers 4 amplitudes … up, down, down, up. … So the amplitude is 1 cm.