Question

In music, middle C has a frequency of about 256 Hz - the precise frequency depends on the tuning scheme. How does the wavelength of a middle C note propagating through air compare to the size of a typical human body? How does the wavelength of the same note propagating through water compare to the human body? What frequency of sound in air has a wavelength nearly the size of a human head? This size is important because we have diminished ability to determine the direction to a source of this tone.

Answer 1

Ans:

a)     The relationship of the speed of sound, its frequency, and wavelength is the same as for all waves:

      

                                         -------------------------------1

   where is the speed of sound, is its frequency, and is its wavelength.

we have been given middle C has frequency in 256 Hz  

as temperature is not given we assume speed of sound as 343 m/s at 20 degree celsius

            put in equation

                            343=256 x

                          =343/256 m =1.34 m  

typical human body has Interestingly, the global average height is 159.5 cm for women, and 171 cm for men that is the wavelength of middle C note is little shorter than the height of humans

b) now the same not is propagating through water keeping same frequency . It travels at 1,481 m/s in

      apply same equation   1 to this and put values

                               1481=256 x

                              = 1481/256    =5.785 m

we can see the wavelength has been increased. it is approximately 4 times greater than height of a human body.

c) The average human head is 6 to 7 inches wide and 8 to 9 inches long. suppose we take higher values 7 inch wide

    7 inch is 17.5 cm i.e 0.175 m

     =0.175 m

     speed of sound in air

        using equation 1 and putting values we get

                    343m/s =f x 0.175 m  

                    f = 1960 Hz

             When sounds are light treble sounds (over 1 kHz), the wavelength plays an essential role for the brain in determining the sound direction. These sounds all have a limited wavelength of less than 30 cm

When a person hears sounds of limited wavelengths, the head functions as a screen. If the sound comes from a direction to the right of the face, the head will prevent the sound waves from reaching the left ear. Deep base sounds, on the other hand, have a larger wavelength, and the head will not prevent the sound waves from reaching both ears.