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Two musicians are playing the same instruments. The first one emits the sound with correct wavelength 58 cm while the second one is off, and the wavelength is 5 mm longer.
a) What is the frequency of the beats when they play together?
b) By how much does the second musician need to change her instrument’s wavelength so that thefrequency of the beats is reduced to 1 Hz?

Respuesta :

Answer:

Explanation:

Given

Wavelength of first musician [tex]\lambda _1=58\ cm[/tex]

Wavelength of second musician [tex]\lambda _2=58.5\ cm[/tex]

Frequency of first musician [tex]\nu _1=\frac{v}{\lambda _1}[/tex]

where v=velocity of sound

[tex]\nu _1=\frac{330}{0.58}=568.96\approx 569\ Hz[/tex]

[tex]\nu _2=\frac{330}{0.585}=564.102\ Hz[/tex]

Frequency of beat [tex]\nu _1-\nu _2=4.898\ Hz[/tex]

(b)If beat frequency is reduced to 1 Hz then

[tex]|\nu _1-\nu_2|=1[/tex]

[tex]569-\nu_2=\pm 1[/tex]

[tex]\nu _2=570 or 568\ Hz[/tex]

for [tex]\nu _2=568\ Hz[/tex]

[tex]\lambda _2=58.09\ cm[/tex]

[tex]\nu _2=570\ Hz[/tex]

[tex]\lambda _2=57.89\ cm[/tex]

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