Question

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drawing waves practice

1. define the following terms:

wavelength:
amplitude:
frequency:
crest:
trough:

1. sketch waves with the following characteristics. draw these on graph paper. measurements must be exact. (🞄 square: ≈ 1 cm)

a. 3 cycles of a wave having a wavelength of 5 cm and an amplitude of 2 cm.
b. 2 cycles of a wave with a wavelength 2 cm and an amplitude of 5 cm.
c. 1 cycle of a wave with a wavelength of 10cm and an amplitude of 1 cm.
d. 4 cycles of a wave with a wavelength of 4 cm and an amplitude of 4cm.
e. 3 cycles of a wave with a wavelength of 2 cm and an amplitude of 3 cm.
f. 2 cycles of a wave with an amplitude of 6cm and a wavelength of 3 cm.

1. solve the following problems using your equations!!!

a. what is the velocity of a wave having a frequency of 3 hz and a wavelength of 2 meters.
b. what is the frequency of a wave traveling at a velocity of 100m/s with a wavelength of 10 meters?
c. what is the velocity of a wave if it has the wavelength of 3 meters and a frequency of 9 hz?
d. what is the wavelength of a wave traveling at a velocity of 25m/s having a frequency of 5 hz?
e. how long would a 6 hz wave traveling at a velocity of 36 m/s be in meters?

Explanation:

Step1: Recall wave velocity formula

Wave velocity $v = f \lambda$, where $f$ = frequency, $\lambda$ = wavelength.

Step2: Solve 3a

Substitute $f=3\ \text{Hz}$, $\lambda=2\ \text{m}$ into formula:
$v = 3 \times 2 = 6\ \text{m/s}$

Step3: Solve 3b

Rearrange formula to $f = \frac{v}{\lambda}$. Substitute $v=100\ \text{m/s}$, $\lambda=10\ \text{m}$:
$f = \frac{100}{10} = 10\ \text{Hz}$

Step4: Solve 3c

Substitute $f=9\ \text{Hz}$, $\lambda=3\ \text{m}$ into $v = f \lambda$:
$v = 9 \times 3 = 27\ \text{m/s}$

Step5: Solve 3d

Rearrange formula to $\lambda = \frac{v}{f}$. Substitute $v=25\ \text{m/s}$, $f=5\ \text{Hz}$:
$\lambda = \frac{25}{5} = 5\ \text{m}$

Step6: Solve 3e

Use $\lambda = \frac{v}{f}$. Substitute $v=36\ \text{m/s}$, $f=6\ \text{Hz}$:
$\lambda = \frac{36}{6} = 6\ \text{m}$

Answer:

3a. 6 m/s
3b. 10 Hz
3c. 27 m/s
3d. 5 m
3e. 6 m