Hello Ssam.
Have you had complaints from neighbors already? Whisperrooms are designed for hearing tests. Have you ever had one? Heres the deal. They put you in this booth, put a pair of headphones on you, and play VERY low level sounds at various frequencies to see what you hear. Usually, these booths are in a hearing doctors "facility", which could be anything from a Mall storefront, to an individual building. The booth is designed to keep out sound that may mask the low level sounds. However, since this booth is in a quiet room already, it is sounds OUTSIDE the building that are the point of the booth...sirens, helicopters, planes, busses, traffic, and things of that nature. However, by the time these sounds infiltrate the room, they have already decreased in amplitude, to an average that the designers have determined is "normal" within a room. Since you have headphones on, this is a second line of defense against intruding sound as well. Needless to say, they are NOT designed to keep HIGH SPL sounds from transmitting FROM the booth into the surrounding room, although they are rated for speech level sounds from transmitting. It MAY muffle a sax, to the point where your concrete walls will have enough transmission loss to prevent transmission from occuring, but thats impossible to say.
The ONLY way to know what you are generating in SPL for sure, is to play while someone takes sound level readings on a Sound Level meter, then compare it to the specs on the whisperoom doc's. Even then, you are still pretty much guessing about transmission through the concrete walls. You would have to measure the sound TRANSMITTING through the concrete envelope into an adjacent space to know "concretely"
For absolute guaranteed results, a booth with a TRANSMISSION LOSS RATING to exceed what you are generating would have to be built. Not an easy task. Especially if you wanted it to be dismantled for moving to another location. For one, a booth with high spl transmission loss will be EXTREMELY heavy, as a TWO LEAF-MASS AIR MASS assembly with one leaf decoupled is the best bang for the buck assembly for reducing sound transmission. This means floor, walls, and ceiling. In terms of generally speaking, this would be an assembly with one or two framing assemblies, with an exterior mass of at least 2 layers of 5/8" drywall, a minimum hermetically sealed airgap of 4" filled with batt insulation(more if possible), and a decoupled interior leaf of at least 2 layers of drywall(you may substitute MDF for drywall, a massive door(OR 2 depending on LOW FREQUENCY TL requirements) with double seals, and then, the granddaddy of the solution delimas...ventilation. This is why Whisperoom designs are NOT suitable for high spl TL. They couldn't possibly build a PORTABLE unit with the mass and decoupling required, as it would indeed be so heavy as to make shipping extremely expensive, difficult to build as a portable product, and ventilation requirements which would require venting to exterior sources. But these are my own "opinions" and suffer from lack of information on your apartment envelope TL, and your sound generating SPL facts.
fitZ