Dr Richard Alexander (G44B)

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Presentation transcript:

Dr Richard Alexander (G44B) PA114 Waves and Quanta Unit 2: Waves (Problem solving) Tipler, Chapters 15 & 16 www.astro.le.ac.uk/~rda5/PA1140 Dr Richard Alexander (G44B)

Problem solving lecture - Wave definitions - Standing waves and beats - Wave equation - Wave energy - Wave velocity

The wave function for a wave on a string is given by: - In which direction does the wave travel? - What is the wave speed and wavelength? - What is the maximum transverse speed of an element of the string?

Show that the superposition of two identical waves travelling in opposite directions is a standing wave

Trig identities:

Standing wave

Show that the superposition of two waves with different frequencies results in beats

Note heard at mean of the two frequencies, modulated (beats) at difference between freqs.

A wave on a string has mass density m and is described by the wave function: Show that this is a solution of the wave equation (b) By considering the stretching and transverse velocity of the string, show that energy propagates along the string at the wave speed.

A piano wire is 1 m long, weighs 1 g, and is put under a tension of 40 N. Find the frequency of the first 3 harmonics of the wire. What tension would have to be placed on the wire to make the fundamental middle C (262 Hz)?