Question

In: Physics

A square membrane has all four sides (length a) tightly clamped. Some of its vibrational modes...

A square membrane has all four sides (length a) tightly clamped. Some of its vibrational modes are also dampened by a clamp placed at the center of the membrane. Find the first four distinct vibrational frequencies of this "square drum."

Solutions

Expert Solution


Related Solutions

Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°).
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,
determine the symmetry types for all vibrational modes of square-planar molecules and whether the mode would...
determine the symmetry types for all vibrational modes of square-planar molecules and whether the mode would be IR active or Raman active or neither. show the drawings. HINT the symmetries of vibrational modes should be analogous to the symmetries of SALCs.
Let S be the square centered at the origin with sides of length 2, and C...
Let S be the square centered at the origin with sides of length 2, and C be the unit circle centered at the origin. (a) If you randomly throw a point on S, what is the probability that it will lie in C? Ans: 0.785 (b) Describe how you could use simulation to estimate the probability in part (a). (c) How can you use simulation to estimate a? For part b and c, there maybe a need to generate random...
A square loop of wire with sides of length 34 cm is in a uniform magnetic...
A square loop of wire with sides of length 34 cm is in a uniform magnetic field perpendicular to its area. Part A If the field's strength is initially 110 mT and it decays to zero in 0.011 s , what is the magnitude of the average emf induced in the loop? Part B What would be the average emf if the sides of the loop were only 17 cm ? Express your answer using two significant figures.
Four charges of magnitude +q are placed at the corners of a square whose sides have...
Four charges of magnitude +q are placed at the corners of a square whose sides have a length d. What is the magnitude of the total force exerted by the four charges on a charge Q located a distance b along a line perpendicular to the plane of the square and equidistant from the four charges? Ans: bqQ/πε 0 (b2 + d2 / 2) how to get this answer?
4. Define the width of a rectangle as the longest length of its sides. Given a...
4. Define the width of a rectangle as the longest length of its sides. Given a closed rectangle A in Rn and a partition P of A, define the mesh of P as the maximum width of its subrectangles. Prove that a bounded function f : A → R is integrable on A if and only if, for every > 0, there is a δ > 0 such that U(f, P) − L(f, P) < for every partition P of...
In the figure, a square of edge length 22.0 cm is formed by four spheres of...
In the figure, a square of edge length 22.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.50 g, m3 = 1.40 g, and m4 = 4.70 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.40 g?
In the figure the four particles form a square of edge length a = 6.40 cm...
In the figure the four particles form a square of edge length a = 6.40 cm and have charges q1 = 8.91 nC, q2 = -19.0 nC, q3 = 19.0 nC, and q4 = -8.91 nC. What is the magnitude of the net electric field produced by the particles at the square's center?
In the figure four particles form a square with edge length a = 4.54 × 10-2...
In the figure four particles form a square with edge length a = 4.54 × 10-2 m. The charges are q1 = q4 = 2.20 × 10-15 C and q2 = q3 = q. (a) What is q if the net electrostatic force on particle 1 is zero? (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? Choose the answer for part (b) from the menu in accordance to...
Suppose that a triangle has sides of length a = 15 cm, b = 37 cm,...
Suppose that a triangle has sides of length a = 15 cm, b = 37 cm, and c = 29 cm, then α = _______, β = ______., and γ =______ . Carefully round your answers to the nearest tenth of a degree, do not include units in your typed answers.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT