Answer to Question #140734 in General Chemistry for Steven Rakos

Question

The frequency of the middle E note on a piano is 329.63 Hz. What is the wavelength of this note in centimeters? The speed of sound in air is 343.06 m/s.

Answer 1

Q140734

The frequency of the middle E note on a piano is 329.63 Hz. What is the wavelength of this note in centimeters? The speed of sound in air is 343.06 m/s.

Solution: 

In question, we are given the frequency of the middle E note and we are also provided the speed of the sound. We can use the formula which relates the frequency and wavelength for finding the wavelength of the middle E note. 

The formula is 

 v = f * λ

  

where v is the speed of sound (m/s)

 f is the frequency (Hz or s-1 ) 

 and λ is the wavelength ( m ) 

Step 1: Find the wavelength of the note. 

Substitute, v = 343.06m/s and f = 329.63Hz in the formula we have 

343.06m/s = 329.63 s^-1 * λ 

divide both the side by 329.63 s-1  

343.06m/s/ 329.63 s-1  =  329.63 s^-1 * λ / 329.63 s-1

1.0407 m = λ ; 

Hence, wavelength (λ) = 1.0407 m. 

Step 2: Convert the wavelength to ‘centimeters’ 

In question, we are asked to find the wavelength in centimeters. 

We can use the conversion factor, 1m = 100cm for converting the wavelength to centimeters. 

Wavelength in ‘cm’ = 1.0407 m *  100cm/1m = 104.07 cm 

In question, we are given 329.63 Hz in 5 significant figure, so our final answer must also be in 5 significant figure.

104.07 cm is already in 5 significant figure.

 Hence the frequency of the middle E note in centimeters is 104.07 cm