Question

If you have ever inhaled helium (a trick you should only do carefully) and then try to speak, you notice your voice sounds very different.
    (A) what is the speed of sound in helium? What is the ratio of that speed to the speed in air?
    (B) Assuming the wavelength is set by the person making the sound (whose internal dimensions set the boundary conditions) what is the ratio of the new pitch to the old pitch?
    (C) What fraction of an octave is your answer to B?

Answer 1

(A) Speed of sound in Helium V_He = 1007 m/s

V_He / V_air = 1007 / 343 = 2.94

(B) old pitch = frequency of sound in air = V_air / λ = 343/λ

new pitch = frequency of sound in Helium = V_He / λ = 1007/λ

new pitch / old pitch = (1007/λ) / (343/λ) = 2.94

(C) Fraction of octave = 2.94/8 = 0.3675

Answer 2

a) Speed of Sound in helium \(=\mathrm{c} 1=1007 \mathrm{~m} / \mathrm{s}\)

Speed of sound in air \(=\mathrm{c} 2=343 \mathrm{~m} / \mathrm{s}\)

\(\Rightarrow>\) ratio \(=1007 / 343=2.93\)

b) let lambda be the wavelength=>

\(\lambda=\mathrm{c} / \mathrm{v}\) where \(\mathrm{v}\) is the frequency

So, c1(helium)/c2(air) = v1(old pitch)/v2( new pitch)

\(\Rightarrow\)

v2( new pitch)/ v1(old pitch) \(=c 2 / c 1=343 / 1007=0.34\)

c) 1 octave \(=2\) times of frequency

\(=>0.5\) fraction of an octave is answer to \(\mathrm{B}\)