Finding upper and lower bound superposition frequencies of ultrasound pulses

[Mugen112]

Homework Statement

Ultrasound pulses of with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500m/s . The spatial length of each pulse is 12 mm.

a) How many complete cycles are in each pulse?

b) What is the lower bound of the range of frequencies must be superimposed to create each pulse?

c)What is the upper bound of the range of frequencies must be superimposed to create each pulse?

Homework Equations

ΔX=ΔtV
f=1/T

The Attempt at a Solution

a) Δt= 12mm/1500 = 8 * 10^-6
T = 1/f
T = 1/10^6 = 10^-6

So... (8 * 10^-6)/(10^-6) = 8 full cycles in each pulse

b) and c) I have no idea... All I have is..

Δf = 1/Δt = 125,000 Hz.. How do I find the upper/lower bound?

 

[Redbelly98]

It looks like the range of frequencies will cover a 125,000 Hz range, centered on 1.000 Mhz. From that you can figure out the lowest and highest frequencies in the range.