Activity The Universal Wave Equation
In a previous activity we determined what characteristics affect the speed of a wave. Now you will determine the speed of a
wave itself. Set up your spring along the floor with a fixed length.
1) Determine the speed of a pulse sent down the spring using a metre stick to measure the distance Δd traveled by the
pulse and a stopwatch to measure the time t that the pulse takes. (Rearranging the equation Δd = vt, the speed of the
∆𝑑
pulse can be calculated: 𝑣 = , where v is speed in m/s, Δd is the length of the spring in m, and t is the time in s.
𝑡
Record Δd, t and v in the chart below)
2) Without changing the length of the spring, create a standing wave pattern as shown below (pg. 487) which is a
steady, repeating wave motion with a point in the middle of the spring experiencing no movement at all. The
frequency of oscillation of this wave can be measured by observing the peaks (the points on the spring experiencing
maximum displacement) and counting the # of complete oscillations they make in 10 s and then dividing by 10.
Record the frequency f (in cycles/s) and the wavelength λ (in m, equal to the length of the spring) in the chart below,
and then calculate the product of the frequency and wavelength (i.e. f × ).

3) Repeat steps 1 and 2 for two more different spring lengths, and complete the chart.
Δd = Spring
Length (m)
Time t (s)
Speed v = Δd/t
(m/s)
 (m)
4) Compare the calculated speeds v with the results for f×.
f (cycles/s)
f× (m/s)
State any patterns, if any are observed.
Wave Equation (pg. 443) Write the universal wave equation. State what each variable represents and its units.
Homework:
pg. 445 #1b
Dolphins have a large repertoire of sounds that can be classified under two general types: those sounds used to locate objects,
termed echolocation (sonar), and those emitted to express emotional states. They emit pulses and clicks which have a
frequency of typically 130 kHz. Given that the speed of sound is 344 m/s, find the wavelength of the emitted pulse.
pg. 445#2b
Bat’s sonar abilities allow them to detect the difference in objects as close as 0.3 mm. The typical frequency range of bat
sounds lies around 30 kHz. Calculate the wavelength of the sound given the speed of sound of 340 m/s.
pg. 474 #26
The frequency of a note is 440 Hz. Find the wavelength of the sound given that the speed of sound is (a) 332 m/s, (b) 350
m/s, (c) 1225 km/h
pg. 474 #29
𝜆
If is 0.85 m and the frequency is 125 Hz, find (a) the wavelength, (b) the period of the wave, (c) the velocity of the wave.
4
pg. 474 #31
Find the frequency and velocity given that the wavelength is 75 cm for the following periods (a) 0.020 s, (b) 15.0 ms, (c) 2.0
minutes, (d) 0.6 hours
Drawing Periodic Waves
Aspects of Periodic Waves (page 442)
A periodic wave is a continuous, repeating wave pattern.
1) Imagine taking a single snapshot in time of a periodic wave (transverse) traveling along a spring. Draw a displacementposition graph for this wave that is 3 wavelengths long with an amplitude of 3 cm and a wavelength of 8 cm in the space
below. Label: 3 different ’s, a crest, a trough and the amplitude. 1 box = 1 cm.
2) Imagine tracking the displacement of a single point on a spring as a periodic wave travels through it. Draw a displacementtime graph for a periodic transverse wave that is 3 cycles long with an amplitude of 4 cm and a period of 1.0 s in the space
below. Label: 3 different T’s and the amplitude. 1 box = 1 cm, 1 box = 0.1 s
3) How would you determine the amplitude of a longitudinal wave? Explain how if you attached a piece of tape to the spring.