Mechanical Wave Worksheet

1. Sound waves travel through air near room temperature with a speed of 345 m/s. Since we are partial to breathing air and our ears are close to our mouth and nose, most of the sound waves that we hear come to us through the air. Audible sound ranges from 20 Hz to 20,000 Hz. Find the wavelength range of sounds that we can hear. Answer using three significant digits.

Listen to and see the audible spectrum

Photo by Pixaby / Public Domain

2. A person dips the tip of his finger in the water 3.0 times a second. The distance between adjacent crests of the waves produced is 0.12m. What is the speed, period and frequency of waves produced in the water?

Photo by Augustin Ruiz / CC-BY 2.0

3. Ultrasound imaging can detect details in a human being of about the size of the ultrasound wavelength. The higher the frequency, the greater the resolution. What is the wavelength of a 12 MHz ultrasonic wave if the soft tissue propagation velocity is 1540 m/s?

Photo by Wolfgang Moroder / CC-BY-SA 3.0

4.Mechanical waves require a medium in order to travel. List three examples of mechanical waves.

5. If the speed of sound through air is 340 m/s, what is the frequency of “middle C” on the piano if its wavelength is 1.3 m?

 Photo by Arjun / Public Domain

6. The “TeenBuzz’ is a ringtone that older adults can’t hear, but younger ears can. This could come in handy should your phone ring during class. Find the “TeenBuzz” frequency if the wavelength through air is 2.0 cm. Use 340 m/s for the speed of sound waves in air.

TeenBuzz

7. On stringed instruments like the piano, guitar or violin, the strings will vibrate at more than one frequency at the same time. The lowest frequency, a function of the length of the string, is called the fundamental frequency or the first harmonic. The second harmonic is twice the fundamental frequency. The third harmonic in this harmonic series is three times the fundamental frequency, etc. . . Remember, the string is vibrating at all these frequencies at the same time and together they add a richness (timbre) to the tone produced. Suppose the fundamental frequency on a guitar string is 220 Hz and the speed of sound through air is 345 m/s, find the wavelength of the first harmonic. Then determine the frequency and wavelength of the second and third harmonics.

8. Musical notes that are an octave apart on the piano are of interest as well. The higher of the two notes an octave apart is twice the frequency of the lower note. A1 has a frequency of 55 Hz. A2 is 110 Hz. Find the frequency of A3 and A4. What is the ratio of the frequencies of notes that are three octaves apart? How many times longer is the wavelength of a note that is two octaves lower?

Physics of Music