Chapter 6 Help Please

Question

a). Consider the wave with a speed of 4.0 x 10³­ m/s and frequency of 3.2 MHz (please note: prefix M stands for Mega, which is 10⁶). Calculate the wavelength of this wave. Show your work.



b). Consider another wave of a speed 3x10⁸ m/s and wavelength of 550 nm (please note: prefix n or nano means 10^-9). Calculate the frequency of this wave. Show your work.

Answer 1

Di,

A. Both of these problems use the same 3 variables and a single equation--

1. frequency (in MHz--1.0 X10^6 cycles/second),
2. wavelength (in nm -- 1.0X10^-9 meters)
3. speed of the wave (m/s).

The three are related in a single equation: λ= v/f which can also be written λ ⋅ f= v

If you forget the equation, dimensions can help you remember the connection

wavelength (m/cycle) ⋅frequency (cycles/s) = velocity (m/s)

B. Once you have the foundational equations doing the two problems is relatively straightforward.

1. Part a - you are solving for wavelength. Substitute both known variables into the equation. You can use either form, but the λ =f /v is most helpful.

λ = 4.0.x10³ m/s / 3.2x10⁶ s/cycle = 1.25x10^-3 m/cycle = 1.25 x 10 ^-3 Hz = 1.3 Hz (2 sig. fig)

2. Part b. In this instance you are trying to find the frequency.

The second form of the equation is more helpful λ ⋅ f= v That can easily be dividing on both sides by λ which isolates f.

Assuming you do that f=v/λ Substitute your known variables, and convert nm to m.

f=( 3x10⁸ m/s ) / (550 nm/cycle x 1.0^-9 m/nm).

**Be careful to keep the whole wavelength in the denominator.

f= frequency = 5.45 x 10 ¹⁷ cycles/sec.

With only one significant figure, the frequency is 5 x 10 ¹⁷ Hz

C. Key things to pay attention to:

1. What am I finding?
2. Which form of the equation helps me get that most easily?
3. What are the prefixes involved and what conversions are necessary?
4. Do my units check out?