Average Power of Waves on Strings Practice Problems

A thin steel cable with 2.0 mm diameter is hooked up to a vibrating device, which exerts a tension of 8.5 N on the cable. The device vibrates at a frequency of 70.0 Hz, producing waves in the cable with an amplitude of 0.50 cm. Calculate the power output of this device, assuming the waves do not reflect back along the cable. (The density of steel is ρ_steel=7800 kg/m³).

A guitar string is plucked and vibrates with a tension of 180 N. The string has a linear density of 0.050 kg/m. What power value is required to sustain a 440-Hz musical tone if the amplitude of the string’s vibration is 1.2 cm? Hint use: $\bar{P}=2 \pi^{2} \mu v f^{2} A^{2}$

In a physics experiment, two sinusoidal waves are generated along a stretched string, each with the same frequency. The experiment records that one wave carries 1.6 times the power of the other. Calculate the ratio of their amplitudes.

Calculate the average power of ocean waves acting against a small boat anchored near the shore. The waves have an amplitude of 0.40 m, a wavelength of 5.0 m, and a period of 6.0 s.

A string of mass 5 g and length 1.25 m is tightly attached to a mechanical vibrator at one end and to a fixed support at the other end. The mechanical vibrator generates traveling waves. The traveling wave is modeled with the wave function y = 6 mm (sin { [1.5π (rad/m) x] + [90π (rad/s) t] } ). What is the i) tension (T) in the string and the ii) average power (P_av) transmitted by the traveling wave?