Standing waves

Pick a harmonic on a string or in a pipe and see where the nodes fall — then drive it from a signal generator, find the frequencies at which it resonates, and listen to it.

f —

λ —

v —

L —

The apparatus

Length L—

Hanging mass—

String—

wave speed v

—

The harmonic

frequency f

—

wavelength λ

—

length in wavelengths

—

compared with the first harmonic

—

nodes, counting the ends

—

antinodes

—

Points P and Q

P, from the left-hand end

—

Q, from the left-hand end

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amplitude at P, as a fraction of the largest

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amplitude at Q, as a fraction of the largest

—

phase difference

—

These move P, the last point you dragged:

Resonance curve

Show the whole curve

readings taken

largest so far

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Every change of the frequency is a reading. Change the damping and the old trace stays, faded, so the two can be compared.

Sound

Volume60%

Overlays

The envelope — how far each point swings Label the nodes N and antinodes A The two travelling waves it is made of The air itself, moving Pressure, drawn to the same height A ruler along the length